Area between 2 curves
Author: G. Battaly, WCC

To find the area between 2 curves, we might like to start by finding the area below each of the 2 curves, and then subtracting.  However, this only works if the area is found using the definite integrals with the same upper and lower limits.  So, start by finding the limits.  Then proceed as below.

"If"  is the area below f(x), "Ig" is the area below g(x), and "Ih" is the area below h(x), where h(x) = g(x) - f(x) 
Use the play and pause buttons to start the construction sequence.

f(x) = x^(2)
g(x) = 4 - x^(2)
B = Intersect(f, g, 2)
Ig = Integral(g, 0, 1.4142135623730951)
If = Integral(f, 0, 1.4142135623730951)
h(x) = g(x) - f(x)
Ih = Integral(h, 0, 1.4142135623730951)
Ibetw: Ig - If
Int = IntegralBetween(g, f, 0, sqrt(2))
a = 1.41 (slider from 0 to 1.41, step 0.001)
A: (a, g(a))
C: (a, f(a))
i = Segment(A, C)
b = IntegralBetween(g, f, 0, 1.41)